The math behind survival analysis and far reaching applications

Survival analysis is a branch of statistics that analyses time-to-event data, where the variable of interest is the time it takes for a certain event to occur. It helps us answer questions like: - How long until something happens? - What affects the timing of the event? While most commonly used in medicine—to study patient survival or treatment efficacy—the same mathematical tools apply across fields as diverse as engineering, economics, sociology and beyond. In this talk I will introduce the mathematical foundations of survival analysis, illustrating how math can help us understand counterintuitive phenomena, providing powerful tools to prevent data misinterpretation and quantify estimation uncertainty. We will discuss how censored data—where we don’t observe the actual event time poses unique challenges, and how survival analysis allows us to extract meaningful conclusions from such imperfect observations.